If you have access to your basement crawl space and attic you should be able to run wires without having to cut patch any drywall.
Run ethernet from basement to attic.
For the horizontal portion of the cable run this can involve drilling holes in the joists where the cable will pass.
You want to run solid cable in the walls attic between your terminations jacks.
Here i have mentioned the needed tools for running network cables from basement to second floor before process steps after process steps and other useful info.
If the rooms in question are wired for coax you may be able to sneak the ethernet cable down the wall through the existing hole in the top plate of the wall s.
Attach the wire or cable to a fish tape or coat hanger using electrical tape and feed it into the hole until it reaches the opening at the other end.
If you re working from the attic you can drop a weighted string down wall cavity then attach the wire to the string and pull it through.
From inside the living space position the bit against the wall directly above if accessing from attic or below if accessing from basement the desired location of the service the cable will provide.
When adding or replacing wiring in finished walls most electricians will attempt to make the horizontal portion of the cable run in the unfinished attic or basement crawlspace areas looping the cable down or up through the wall cavity across the floor or ceiling joists then vertically through another stud cavity to the next wall box opening.
There are plenty of places online that sell it by the foot or just go buy a spool at lowes depot.
Run the wire or cable to its destination.
When necessary use existing ducts or pipe runs to get wires from the attic into the basement.